My and your info both seem to agree that the Amaj chord is not in the Dm key, yet the Amaj sounds good to me and presumably others. Not sure if I understand this.
Actually it kinda sorta it, even though it is buried deep in theory and sounds like a pile of crap. There is a strange, wild chord called a Minor Major Seventh which is composed of the Root, Minor Third, Perfect Fifth, and Major Seventh. In the key of Dm, it would be D, F, A, C#. I don't know where you'd use it (I never would other than maybe a passing tone) but some of the jazz guys may have used one. Play a minor 7th and sharp the top note. It is truly cacophonous, but discordant harmony usually is.
You're both not quite correct. A major most certainly is in the key of D minor. It's the V (dominant) chord. Typically that would be a dominant 7th chord, but not always.
The seventh scale degree in a minor key is often raised, creating that leading tone to the tonic which also turns the chord built on the 5th scale degree into a major chord, giving us a stronger V-I cadence.
That's where the Harmonic Minor scale comes from.
The reason why the Major V chord in a minor key sounds right is because you're used to hearing it; 300 plus years' worth of it has been pounded into your ears.
That m/M7 chord ís an entirely different beast altogether. It is what you get if you build a 7th chord on the root of the Harmonic Minor scale.
Also whoever said that the Aeolian Mode is just the minor scale is not quite correct either. The natural minor scale and Aeolian Mode might have all the same notes, but the difference is one of context.
"Key" and "Mode" are not interchangeable.
Music based on functional harmony strongly relies on the V - I cadence and that is true of minor keys as well.
Modal chord progressions seem to be more linear and the chords are not functional like in tonal music. The typical Aeolian cadence is bVI - bVII - I.